Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independence Heuristic

Abstract

For parameters $n,\delta ,B,C$, we obtained a sharp asymptotic formula for the number of $(n+\lfloor n^{\delta }\rfloor {)}^2$-dimensional binary contingency tables with non-uniform margins taking values of $\lfloor BCn\rfloor$ and $\lfloor Cn\rfloor$. Furthermore, we compared our sharp asymptotics with the classical independence heuristic estimate and proved that the independence heuristic overestimates by a factor of $e^{\Theta (n^{2\delta })}$. Our comparison is based on the analysis of the correlation ratio and an explicit bound for the constant in $\Theta$ is also obtained.

Minor typos corrected and references updated as suggested by referee, to appear in Contributions to Mathematics

References in corpus (1)

• On Properties of Random Binary Contingency Tables with Non-Uniform Margin